OFFSET
0,4
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
FORMULA
a(n) = n! * sum(k=0..n, (binomial((n-2)/2, (n-k)/2) * 2^(n-k-1) * ((-1)^(n-k)+1))/k!).
a(n) ~ (2*n)^(n-1/3) / (sqrt(3)*exp(n-3/4*(2*n)^(1/3))). - Vaclav Kotesovec, Jun 02 2013
MATHEMATICA
CoefficientList[Series[Exp[x/Sqrt[1-4*x^2]], {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Jun 02 2013 *)
PROG
(Maxima)
a(n):= n!*sum((binomial((n-2)/2, (n-k)/2)*2^(n-k-1)*((-1)^(n-k)+1))/k!, k, 0, n);
(PARI) x='x+O('x^66); /* that many terms */
egf=exp(x/sqrt(1-4*x^2)) /* = 1 +x +1/2*x^2 +13/6*x^3 +49/24*x^4 +... */
Vec(serlaplace(egf)) /* show terms */ /* Joerg Arndt, Apr 22 2011 */
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Kruchinin, Apr 16 2011
STATUS
approved